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The Pythagorean Theorem which applies to right triangles states that:
a and b are the lengths of the legs while c is the length of the hypotenuse.

In the Cartesian plane they are:

The points are have coordinates (x,y)

This means
 (x_a,y_a) are the coordinates of the first point 
and (x_b,y_b) are the coordinates of the second

So in the problem:
(x_a,y_a)=(2,-2) which are the coordinates of P
(x_b,y_b)=(-1,2) which are the coordinates of P

We substitute this to the Pythagorean theorem
9+16=c^2 \\ 25=c^2 \\ 5=c

The triangle that will be formed has a very common Pythagorean triple which is (3,4,5).

The length of the hypotenuse (or any length of a side) cannot be less than or equal to 0 so it cannot be -5.

Therefore the length of the line segment when you connect the two points is 5.

0 0 0
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